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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">R</font> being  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Olive" title="b1">A</font> holds <br/> (  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Olive" title="b2">R</font>,<font color="Olive" title="b1">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b2">R</font> &amp;  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <font color="Olive" title="b2">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b2">R</font> &amp;  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Olive" title="b2">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b2">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Olive" title="b2">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b2">R</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font> holds <br/> (  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Olive" title="b1">R</font>,<font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b1">R</font> &amp;  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <font color="Olive" title="b1">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b1">R</font> &amp;  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Olive" title="b1">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b1">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Olive" title="b1">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Olive" title="b1">R</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> )</span><br/>





<a NAME="E1:82"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
<font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#D15" target="_self" title="MSUALG_6:def.15">Def15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:82"/>
 <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_6.html#T44" target="_self" title="MSUALG_6:th.44">Th44</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:82"/>
(  <a href="msualg_6.html#K6" title="MSUALG_6:func.6">InvCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K7" title="MSUALG_6:func.7">StabCl</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> &amp;  <a href="msualg_6.html#K8" title="MSUALG_6:func.8">TRS</a> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K10" title="MSUALG_6:func.10">EqTh</a> <font color="Maroon" title="c3">R</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="ref" href="msualg_6.html#D11" target="_self" title="MSUALG_6:def.11">Def11</a>, <a class="ref" href="msualg_6.html#D12" target="_self" title="MSUALG_6:def.12">Def12</a>, <a class="ref" href="msualg_6.html#D13" target="_self" title="MSUALG_6:def.13">Def13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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